Simplify (-20v)/(-4(v^-1)^3)

$\frac{- 20 v}{- 4 {(v^{- 1})}^{3}}$

Cancel the common factor of $- 20$ and $- 4$ .

Factor $- 4$ out of $- 20 v$ .

$\frac{- 4 (5 v)}{- 4 {(v^{- 1})}^{3}}$

Cancel the common factors.

Factor $- 4$ out of $- 4 {(v^{- 1})}^{3}$ .

$\frac{- 4 (5 v)}{- 4 ({(v^{- 1})}^{3})}$

Cancel the common factor.

$\frac{- 4 (5 v)}{- 4 {(v^{- 1})}^{3}}$

Rewrite the expression.

$\frac{5 v}{{(v^{- 1})}^{3}}$

Simplify the denominator.

Multiply the exponents in ${(v^{- 1})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5 v}{v^{- 1 \cdot 3}}$

Multiply $- 1$ by $3$ .

$\frac{5 v}{v^{- 3}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5 v}{\frac{1}{v^{3}}}$

Multiply the numerator by the reciprocal of the denominator.

$5 v \cdot v^{3}$

Multiply $v$ by $v^{3}$ by adding the exponents.

Move $v^{3}$ .

$5 (v^{3} v)$

Multiply $v^{3}$ by $v$ .

Raise $v$ to the power of $1$ .

$5 (v^{3} v^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 v^{3 + 1}$

Add $3$ and $1$ .

$5 v^{4}$